[seqfan] guessing doubling formulas for sequences

Georgi Guninski guninski at guninski.com
Tue Mar 10 11:17:28 CET 2009

```hi,

i wondered what sequences in OEIS are efficiently computable (after
excluding linear recurrences with constant coefficients because of
triviality).

so i wrote a short program that tries to guess doubling formulas. it is
available under GPL at [1].

by ``doubling formula'' i mean given \$n\$ an near neighbors
\$a_n,a_{n+1}...a_{n+k}\$ compute a_{2 n}

partial *wild guesses* from it for doubling are at [2] and ``degree 2
relations'' of near neighbors are at [3].

by ``degree 2 relations'' i mean find a degree 2 polynomial \$P\$, such
that \$P(a_n,a_{n+1}...a_{n+k})=0\$ holds for \$a_n\$

currently the program tries to guess *rational* doubling formulas.

can someone please give examples of doubling formulas for sequences that
are not rational (probably exponential)?

thanks.

[1] http://www.guninski.com/nmbrz/stefun.sage
[2] http://www.guninski.com/nmbrz/oeis-doubling.html
[3] http://www.guninski.com/nmbrz/oeis-deg2.html

```